A general construction is given of systems of distributions on a Hilbert space. Each system is constructed according to a certain operator and the resulting distributions form a normed space. A canonical representation of these systems is obtained. In a note to follow soon, this construction will be used to obtain the spectral expansions of self-adjoint operators.
Citation Example:Kats G. I. Distributions on a Hilbert Space // Ukr. Mat. Zh. - 1960. - 12, № 1. - pp. 13-24.